Automotive synthetic aperture radar with radon transform

ABSTRACT

A method for using Synthetic Aperture Radar (SAR) to perform a maneuver in a land vehicle is provided. The method includes: receiving digitized radar return data from a radar transmission from a SAR onboard the vehicle; accumulating a plurality of frames of the digitized radar return data; applying a RADON transform to the accumulated plurality of frames of the digitized radar return data and odometry data from the vehicle to generate transformed frames of data for each three-dimensional point, wherein the RADON transform is configured to perform coherent integration for each three-dimensional point, project a radar trajectory onto each three-dimensional point, and project Doppler information onto each three-dimensional point; generating a two-dimensional map of an area covered by the radar transmission from the SAR based on the transformed frames of data for each three-dimensional point; and performing a maneuver with the land vehicle by applying the generated two-dimensional map.

TECHNICAL FIELD

The technology described in this patent document relates generally tosystems and methods for using Synthetic Aperture Radar (SAR) in anautomotive setting and more particularly to systems and methods for nearfield use of SAR in an automotive setting.

Radar is useful in many vehicle applications such as collision warning,blind spot warning, lane change assist, parking assist, and rearcollision warning. One type of radar used is a pulsed radar. In pulsedradar, the radar sends signals in the form of pulses at fixed intervals.Obstacles scatter the transmitted pulses, and the scattered pulses arereceived by the radar. The time between sending a pulse and receiving ascattered pulse is proportional to the distance of the obstacle from theradar. Radar angular resolution can be limited by the physical antennaaperture. Radar angular resolution can be improved by creating a largervirtual aperture. By accumulating information from a moving radar, alarge virtual aperture can be achieved. Synthetic Aperture Radar (SAR)can enable high angular resolution by creating a large syntheticantenna.

SAR uses pulse compression technology and the principle of syntheticaperture to achieve imaging of ground scenes. SAR is typically used onsatellites or aircraft for far field applications such as environmentalmonitoring, resource exploration, surveying and mapping, and battlefieldreconnaissance. The radar returns from SAR are typically processed usingsome form of a fast Fourier transform (FFT).

Conventional SAR processing requires the radar to travel at a straightpath with a constant velocity, assumes far-field operation, and requiresthe unambiguous synthetic antenna with ½ λ spacing, which limits maximalvelocity to: v=F·A, where F is the frame rate, A is the antenna apertureand v is the maximal velocity. As an example, for a frame rate of 30 fpsand an aperture of 4 cm (20 antennas), the maximal velocity is limitedto 1.2 m/s. The automotive environment does not meet these assumptions,limiting the useability of conventional SAR implementations.

Accordingly, it is desirable to provide systems and methods for adaptingSAR for near field application in an automotive environment.Furthermore, other desirable features and characteristics will becomeapparent from the subsequent detailed description and the appendedclaims, taken in conjunction with the accompanying drawings.

SUMMARY

Systems and methods for adapting SAR for near field application in anautomotive environment are provided. In one embodiment, a method forusing Synthetic Aperture Radar (SAR) to perform a maneuver in a landvehicle is provided. The method includes: receiving digitized radarreturn data from a pulsed radar transmission from a SAR onboard the landvehicle; accumulating a plurality of frames of the digitized radarreturn data; applying a RADON transform to the accumulated plurality offrames of the digitized radar return data and odometry data from theland vehicle to generate transformed frames of data for eachthree-dimensional (x, y, z) point, wherein the RADON transform isconfigured to perform coherent integration for each three-dimensionalpoint for which a radar return exists from the pulsed radartransmission, project a radar trajectory onto each three-dimensionalpoint, and project Doppler information onto each three-dimensionalpoint; generating a two-dimensional X-Y map of an area covered by thepulsed radar transmission from the SAR based on the transformed framesof data for each three-dimensional point; and performing an autonomousor semiautonomous maneuver with the land vehicle by applying thegenerated two-dimensional X-Y map.

In one embodiment, the RADON transform includes a range dimension, aDoppler dimension, and a phase dimension.

In one embodiment, the RADON transform is represented by:

${S\left( {x,y,z} \right)} = {\sum\limits_{f = 0}^{F - 1}{\sum\limits_{v = 0}^{V - 1}{\sum\limits_{h = 0}^{H - 1}{\sum\limits_{m = 0}^{M - 1}{\sum\limits_{n = 0}^{N - 1}{{s\left( {n,m,h,f} \right)}e^{{- 2}\pi{{jR}({m,f,x,y,z})}\frac{n}{N}}e^{{- 2}\pi j{D({m,f,x,y,z})}\frac{m}{M}}e^{{- 2}\pi j{P({m,h,v,f,x,y,z})}}}}}}}}$

wherein: R(m, f, x, y, z) represents a range dimension, D(m, f, x, y, z)represents a Doppler dimension, P(m, h, f, x, y, z) represents a phasedimension, m=sample index, n=chirp index, h=horizontal antenna index,v=vertical antenna index, f=frame index, x=x-axis location, y=y-axislocation, z=z-axis location, s=sampled signal, N=number of samples,M=number of chirps, H=number of horizontal antennas, V=number ofvertical antennas, and F=number of frames.

In one embodiment, the range dimension of the RADON transform isrepresented by:

${R\left( {m,f,x,y,z} \right)} = {\frac{2\alpha}{c}\sqrt{\left( {{O_{x}\left( {t\left( {m,f} \right)} \right)} - x} \right)^{2} + \left( {{O_{y}\left( {t\left( {m,f} \right)} \right)} - y} \right)^{2} + \left( {{O_{z}\left( {t\left( {m,f} \right)} \right)} - z} \right)^{2}}}$

wherein: c=speed of light, α=chirp slope, t(m, f)=mT_(c)+fT_(f),T_(c)=Chirp repetition interval, T_(f)=Frame repetition interval,O_(x)=Odometry based vehicle position at the x-axis, O_(y)=Odometrybased vehicle position at the y-axis, and O_(z)=Odometry based vehicleposition at the z-axis.

In one embodiment, the Doppler dimension of the RADON transform isrepresented by:

${D\left( {m,f,x,y,z} \right)} = {\frac{2}{\lambda}\frac{\begin{matrix}{{\left. {{O_{x}\left( {t\left( {m,f} \right)} \right)} - x} \right)O_{Vx}} +} \\{{\left( {{O_{y}\left( {t\left( {m,f} \right)} \right)} - y} \right)O_{Vy}} + {\left( {{O_{z}\left( {t\left( {m,f} \right)} \right)} - z} \right)O_{Vz}}}\end{matrix}}{\sqrt{\left( {{O_{x}\left( {t\left( {m,f} \right)} \right)} - x} \right)^{2} + \left( {{O_{y}\left( {t\left( {m,f} \right)} \right)} - y} \right)^{2} + \left( {{O_{z}\left( {t\left( {m,f} \right)} \right)} - z} \right)^{2}}}}$

wherein: t(m, f)=mT_(c)+fT_(f), λ=signal wavelength, T_(c)=Chirprepetition interval, T_(f)=Frame repetition interval, O_(x)=Odometrybased vehicle position at the x-axis, O_(y)=Odometry based vehicleposition at the y-axis, O_(x)=Odometry based vehicle position at thez-axis, O_(Vx)=Odometry based vehicle velocity at the x-axis,O_(Vy)=Odometry based vehicle velocity at the y-axis, andO_(Vz)=Odometry based vehicle velocity at the z-axis.

In one embodiment, the phase dimension of the RADON transform isrepresented by:

${P\left( {m,h,f,x,y,z} \right)} = {{\frac{\frac{\left. {{O_{y}\left( {t\left( {m,f} \right)} \right)} - y} \right)}{\left. {{O_{x}\left( {t\left( {m,f} \right)} \right)} - x} \right)}}{\begin{matrix}\sqrt{1 + \left( \frac{\left. {{O_{y}\left( {t\left( {m,f} \right)} \right)} - y} \right)}{\left. {{O_{x}\left( {t\left( {m,f} \right)} \right)} - x} \right)} \right)^{2}} \\\sqrt{1 + \frac{\left( {{O_{z}\left( {t\left( {m,f} \right)} \right)} - z} \right)^{2}}{\left( {{O_{x}\left( {t\left( {m,f} \right)} \right)} - x} \right)^{2} + \left( {{O_{y}\left( {t\left( {m,f} \right)} \right)} - y} \right)^{2}}}\end{matrix}}h\frac{d_{h}}{\lambda}} + {\frac{\frac{{O_{z}\left( {t\left( {m,f} \right)} \right)} - z}{\sqrt{\left( {{O_{x}\left( {t\left( {m,f} \right)} \right)} - x} \right)^{2} + \left( {{O_{y}\left( {t\left( {m,f} \right)} \right)} - y} \right)^{2}}}}{\sqrt{1 + \frac{\left( {{O_{z}\left( {t\left( {m,f} \right)} \right)} - z} \right)^{2}}{\left( {{O_{x}\left( {t\left( {m,f} \right)} \right)} - x} \right)^{2} + \left( {{O_{y}\left( {t\left( {m,f} \right)} \right)} - y} \right)^{2}}}}v\frac{d_{v}}{\lambda}}}$

wherein: t(m, f)=mT_(c)+fT_(f), λ=signal wavelength, d_(h)=antennahorizontal spacing, d_(v)=antenna vertical spacing, T_(c)=Chirprepetition interval, T_(f)=Frame repetition interval, O_(x)=Odometrybased vehicle position at the x-axis, O_(y)=Odometry based vehicleposition at the y-axis, O_(z)=Odometry based vehicle position at thez-axis, O_(Vx)=Odometry based vehicle velocity at the x-axis,O_(Xy)=Odometry based vehicle velocity at the y-axis, andO_(Vz)=Odometry based vehicle velocity at the z-axis.

In one embodiment, the RADON transform is represented by:

${S\left( {x,y,z} \right)} = {\sum\limits_{f = 0}^{F - 1}{\sum\limits_{v = 0}^{V - 1}{\sum\limits_{h = 0}^{H - 1}{\sum\limits_{m = 0}^{M - 1}{\sum\limits_{n = 0}^{N - 1}{{s\left( {n,m,h,f} \right)}e^{{- 2}\pi{{jR}({m,f,x,y,z})}\frac{n}{N}}e^{{- 2}\pi j{D({m,f,x,y,z})}\frac{m}{M}}e^{{- 2}\pi j{P({m,h,v,f,x,y,z})}}}}}}}}$

wherein:

${R\left( {m,f,x,y,z} \right)} = {\frac{2\alpha}{c}\sqrt{\left( {{O_{x}\left( {t\left( {m,f} \right)} \right)} - x} \right)^{2} + \left( {{O_{y}\left( {t\left( {m,f} \right)} \right)} - y} \right)^{2} + \left( {{O_{z}\left( {t\left( {m,f} \right)} \right)} - z} \right)^{2}}}$${D\left( {m,f,x,y,z} \right)} = {\frac{2}{\lambda}\frac{\begin{matrix}{{\left. {{O_{x}\left( {t\left( {m,f} \right)} \right)} - x} \right)O_{Vx}} +} \\{{\left( {{O_{y}\left( {t\left( {m,f} \right)} \right)} - y} \right)O_{Vy}} + {\left( {{O_{z}\left( {t\left( {m,f} \right)} \right)} - z} \right)O_{Vz}}}\end{matrix}}{\sqrt{\left( {{O_{x}\left( {t\left( {m,f} \right)} \right)} - x} \right)^{2} + \left( {{O_{y}\left( {t\left( {m,f} \right)} \right)} - y} \right)^{2} + \left( {{O_{z}\left( {t\left( {m,f} \right)} \right)} - z} \right)^{2}}}}$${P\left( {m,h,f,x,y,z} \right)} = {{\frac{\frac{\left. {{O_{y}\left( {t\left( {m,f} \right)} \right)} - y} \right)}{\left. {{O_{x}\left( {t\left( {m,f} \right)} \right)} - x} \right)}}{\sqrt{1 + {\left( \frac{\left. {{O_{y}\left( {t\left( {m,f} \right)} \right)} - y} \right)}{\left. {{O_{x}\left( {t\left( {m,f} \right)} \right)} - x} \right)} \right)^{2}\sqrt{1 + \frac{\left( {{O_{z}\left( {t\left( {m,f} \right)} \right)} - z} \right)^{2}}{\left( {{O_{x}\left( {t\left( {m,f} \right)} \right)} - x} \right)^{2} + \left( {{O_{y}\left( {t\left( {m,f} \right)} \right)} - y} \right)^{2}}}}}}h\frac{d_{h}}{\lambda}} + {\frac{\frac{{O_{z}\left( {t\left( {m,f} \right)} \right)} - z}{\sqrt{\left( {{O_{x}\left( {t\left( {m,f} \right)} \right)} - x} \right)^{2} + \left( {{O_{y}\left( {t\left( {m,f} \right)} \right)} - y} \right)^{2}}}}{\sqrt{1 + \frac{\left( {{O_{z}\left( {t\left( {m,f} \right)} \right)} - z} \right)^{2}}{\left( {{O_{x}\left( {t\left( {m,f} \right)} \right)} - x} \right)^{2} + \left( {{O_{y}\left( {t\left( {m,f} \right)} \right)} - y} \right)^{2}}}}v\frac{d_{v}}{\lambda}}}$t(m, f) = mT_(c) + fT_(f)

m=sample index, n=chirp index, h=horizontal antenna index, v=verticalantenna index, f=frame index, x=x-axis location, y=y-axis location,z=z-axis location, s=sampled signal, N=number of samples, M=number ofchirps, H=number of horizontal antennas, V=number of vertical antennas,F=number of frames, c=speed of light, α=chirp slope, λ=signalwavelength, d_(h)=antenna horizontal spacing, d_(v)=antenna verticalspacing, T_(c)=Chirp repetition interval, T_(f)=Frame repetitioninterval, O_(x)=Odometry based vehicle position at the x-axis,O_(y)=Odometry based vehicle position at the y-axis, O_(z)=Odometrybased vehicle position at the z-axis, O_(Vx)=Odometry based vehiclevelocity at the x-axis, O_(Vy)=Odometry based vehicle velocity at they-axis, and O_(Vz)=Odometry based vehicle velocity at the z-axis.

In another embodiment, a system for applying Synthetic Aperture Radar(SAR) in a land vehicle to perform a maneuver is provided. The systemincludes a controller configured to: receive digitized radar return datafrom a pulsed radar transmission from a Synthetic Aperture Radar (SAR)onboard a land vehicle; accumulate a plurality of frames of thedigitized radar return data; apply a RADON transform to the accumulatedplurality of frames of the digitized radar return data and odometry datafrom the land vehicle to generate transformed frames of data for eachthree-dimensional (x, y, z) point, wherein the RADON transform isconfigured to perform coherent integration for each three-dimensionalpoint for which a radar return exists from the pulsed radartransmission, project a radar trajectory onto each three-dimensionalpoint, and project Doppler information onto each three-dimensionalpoint; generate a two-dimensional X-Y map of an area covered by thepulsed radar transmission from the SAR based on the transformed framesof data for each three-dimensional point; and perform an autonomous orsemiautonomous maneuver with the land vehicle by applying the generatedtwo-dimensional X-Y map.

In one embodiment, the RADON transform includes a range dimension, aDoppler dimension, and a phase dimension.

In one embodiment, the RADON transform is represented by:

${S\left( {x,y,z} \right)} = {\sum\limits_{f = 0}^{F - 1}{\sum\limits_{v = 0}^{V - 1}{\sum\limits_{h = 0}^{H - 1}{\sum\limits_{m = 0}^{M - 1}{\sum\limits_{n = 0}^{N - 1}{{s\left( {n,m,h,f} \right)}e^{{- 2}\pi j{R({m,f,x,y,z})}\frac{n}{N}}e^{{- 2}\pi j{D({m,f,x,y,z})}\frac{m}{M}}e^{{- 2}\pi j{P({m,h,v,f,x,y,z})}}}}}}}}$

wherein: R(m, f, x, y, z) represents a range dimension, D(m, f, x, y, z)represents a Doppler dimension, P(m, h, f, x, y, z) represents a phasedimension, m=sample index, n=chirp index, h=horizontal antenna index,v=vertical antenna index, f=frame index, x=x-axis location, y=y-axislocation, z=z-axis location, s=sampled signal, N=number of samples,M=number of chirps, H=number of horizontal antennas, V=number ofvertical antennas, and F=number of frames.

In one embodiment, the range dimension of the RADON transform isrepresented by:

${R\left( {m,f,x,y,z} \right)} = {\frac{2\alpha}{c}\sqrt{\left( {{O_{x}\left( {t\left( {m,f} \right)} \right)} - x} \right)^{2} + \left( {{O_{y}\left( {t\left( {m,f} \right)} \right)} - y} \right)^{2} + \left( {{O_{z}\left( {t\left( {m,f} \right)} \right)} - z} \right)^{2}}}$

wherein: c=speed of light, α=chirp slope, t(m, f)=mT_(c)+fT_(f),T_(c)=Chirp repetition interval, T_(f)=Frame repetition interval,O_(x)=Odometry based vehicle position at the x-axis, O_(y)=Odometrybased vehicle position at the y-axis, and O_(z)=Odometry based vehicleposition at the z-axis.

In one embodiment, the Doppler dimension of the RADON transform isrepresented by:

${D\left( {m,f,x,y,z} \right)} = {\frac{2}{\lambda}\frac{\begin{matrix}{{\left. {{O_{x}\left( {t\left( {m,f} \right)} \right)} - x} \right)O_{Vx}} +} \\{{\left( {{O_{y}\left( {t\left( {m,f} \right)} \right)} - y} \right)O_{Vy}} + {\left( {{O_{z}\left( {t\left( {m,f} \right)} \right)} - z} \right)O_{Vz}}}\end{matrix}}{\sqrt{\left( {{O_{x}\left( {t\left( {m,f} \right)} \right)} - x} \right)^{2} + \left( {{O_{y}\left( {t\left( {m,f} \right)} \right)} - y} \right)^{2} + \left( {{O_{z}\left( {t\left( {m,f} \right)} \right)} - z} \right)^{2}}}}$

wherein: t(m, f)=mT_(c)+fT_(f), λ=signal wavelength, T_(c)=Chirprepetition interval, T_(f)=Frame repetition interval, O_(x)=Odometrybased vehicle position at the x-axis, O_(y)=Odometry based vehicleposition at the y-axis, O_(z)=Odometry based vehicle position at thez-axis, O_(Vx)=Odometry based vehicle velocity at the x-axis,O_(Vy)=Odometry based vehicle velocity at the y-axis, andO_(Vz)=Odometry based vehicle velocity at the z-axis.

In one embodiment, the phase dimension of the RADON transform isrepresented by:

${P\left( {m,h,f,x,y,z} \right)} = {{\frac{\frac{\left. {{O_{y}\left( {t\left( {m,f} \right)} \right)} - y} \right)}{\left. {{O_{x}\left( {t\left( {m,f} \right)} \right)} - x} \right)}}{\begin{matrix}\sqrt{1 + \left( \frac{\left. {{O_{y}\left( {t\left( {mf} \right)} \right)} - y} \right)}{\left. {{O_{x}\left( {t\left( {mf} \right)} \right)} - x} \right)} \right)^{2}} \\\sqrt{1 + \frac{\left( {{O_{z}\left( {t\left( {mf} \right)} \right)} - z} \right)^{2}}{\left. {\left. \left( {{O_{x}\left( {t\left( {mf} \right)} \right)} - x} \right) \right)^{2} + \left( {{O_{y}\left( {t\left( {mf} \right)} \right)} - y} \right)} \right)^{2}}}\end{matrix}}h\frac{d_{h}}{\lambda}} + {\frac{\frac{{O_{z}\left( {t\left( {mf} \right)} \right)} - z}{\sqrt{\left. {\left. \left( {{O_{x}\left( {t\left( {mf} \right)} \right)} - x} \right) \right)^{2} + \left( {{O_{y}\left( {t\left( {mf} \right)} \right)} - y} \right)} \right)^{2}}}}{\sqrt{1 + \frac{\left( {{O_{z}\left( {t\left( {mf} \right)} \right)} - z} \right)^{2}}{\left. {\left. \left( {{O_{x}\left( {t\left( {mf} \right)} \right)} - x} \right) \right)^{2} + \left( {{O_{y}\left( {t\left( {mf} \right)} \right)} - y} \right)} \right)^{2}}}}v\frac{d_{v}}{\lambda}}}$

wherein: t(m, f)=mT_(c)+fT_(f), λ=signal wavelength, d_(h)=antennahorizontal spacing, d_(v)=antenna vertical spacing, T_(c)=Chirprepetition interval, T_(f)=Frame repetition interval, O_(x) 32 Odometrybased vehicle position at the x-axis, O_(y)=Odometry based vehicleposition at the y-axis, O_(z)=Odometry based vehicle position at thez-axis, O_(Vx)=Odometry based vehicle velocity at the x-axis,O_(Vy)=Odometry based vehicle velocity at the y-axis, andO_(Vz)=Odometry based vehicle velocity at the z-axis.

In one embodiment, the RADON transform is represented by:

${S\left( {x,y,z} \right)} = {\sum\limits_{f = 0}^{F - 1}{\sum\limits_{v = 0}^{V - 1}{\sum\limits_{h = 0}^{H - 1}{\sum\limits_{m = 0}^{M - 1}{\sum\limits_{n = 0}^{N - 1}{{s\left( {n,m,h,f} \right)}e^{{- 2}\pi j{R({m,f,x,y,z})}\frac{n}{N}}e^{{- 2}\pi j{D({m,f,x,y,z})}\frac{m}{M}}e^{{- 2}\pi j{P({m,h,v,f,x,y,z})}}}}}}}}$

wherein:

${R\left( {m,f,x,y,z} \right)} = {\frac{2\alpha}{c}\sqrt{\left( {{O_{x}\left( {t\left( {m,f} \right)} \right)} - x} \right)^{2} + \left( {{O_{y}\left( {t\left( {m,f} \right)} \right)} - y} \right)^{2} + \left( {{O_{z}\left( {t\left( {m,f} \right)} \right)} - z} \right)^{2}}}$${D\left( {m,f,x,y,z} \right)} = {\frac{2}{\lambda}\frac{\begin{matrix}{{\left. {{O_{x}\left( {t\left( {m,f} \right)} \right)} - x} \right)O_{Vx}} +} \\{{\left( {{O_{y}\left( {t\left( {m,f} \right)} \right)} - y} \right)O_{Vy}} + {\left( {{O_{z}\left( {t\left( {m,f} \right)} \right)} - z} \right)O_{Vz}}}\end{matrix}}{\sqrt{\left( {{O_{x}\left( {t\left( {m,f} \right)} \right)} - x} \right)^{2} + \left( {{O_{y}\left( {t\left( {m,f} \right)} \right)} - y} \right)^{2} + \left( {{O_{z}\left( {t\left( {m,f} \right)} \right)} - z} \right)^{2}}}}$${P\left( {m,h,f,x,y,z} \right)} = {{\frac{\frac{\left. {{O_{y}\left( {t\left( {m,f} \right)} \right)} - y} \right)}{\left. {{O_{x}\left( {t\left( {m,f} \right)} \right)} - x} \right)}}{\begin{matrix}\sqrt{1 + \left( \frac{\left. {{O_{y}\left( {t\left( {mf} \right)} \right)} - y} \right)}{\left. {{O_{x}\left( {t\left( {mf} \right)} \right)} - x} \right)} \right)^{2}} \\\sqrt{1 + \frac{\left( {{O_{z}\left( {t\left( {mf} \right)} \right)} - z} \right)^{2}}{\left. {\left. \left( {{O_{x}\left( {t\left( {mf} \right)} \right)} - x} \right) \right)^{2} + \left( {{O_{y}\left( {t\left( {mf} \right)} \right)} - y} \right)} \right)^{2}}}\end{matrix}}h\frac{d_{h}}{\lambda}} + {\frac{\frac{{O_{z}\left( {t\left( {mf} \right)} \right)} - z}{\sqrt{\left. {\left. \left( {{O_{x}\left( {t\left( {mf} \right)} \right)} - x} \right) \right)^{2} + \left( {{O_{y}\left( {t\left( {mf} \right)} \right)} - y} \right)} \right)^{2}}}}{\sqrt{1 + \frac{\left( {{O_{z}\left( {t\left( {mf} \right)} \right)} - z} \right)^{2}}{\left. {\left. \left( {{O_{x}\left( {t\left( {mf} \right)} \right)} - x} \right) \right)^{2} + \left( {{O_{y}\left( {t\left( {mf} \right)} \right)} - y} \right)} \right)^{2}}}}v\frac{d_{v}}{\lambda}}}$t(m, f) = mT_(c) + fT_(f)

m=sample index, n=chirp index, h=horizontal antenna index, v=verticalantenna index, f=frame index, x=x-axis location, y=y-axis location,z=z-axis location, s=sampled signal, N=number of samples, M=number ofchirps, H=number of horizontal antennas, V=number of vertical antennas,F=number of frames, c=speed of light, α=chirp slope, λ=signalwavelength, d_(h)=antenna horizontal spacing, d_(v)=antenna verticalspacing, T_(c)=Chirp repetition interval, T_(f)=Frame repetitioninterval, O_(x)=Odometry based vehicle position at the x-axis,O_(y)=Odometry based vehicle position at the y-axis, O_(z)=Odometrybased vehicle position at the z-axis, O_(Vx)=Odometry based vehiclevelocity at the x-axis, O_(Vy)=Odometry based vehicle velocity at they-axis, and O_(Vz)=Odometry based vehicle velocity at the z-axis.

In another embodiment, a non-transitory computer readable media encodedwith programming instructions configurable to cause a processor in aland vehicle to perform a method for using Synthetic Aperture Radar(SAR) to perform a maneuver with the land vehicle. The method includes:accumulating a plurality of frames of the digitized radar return data;applying a RADON transform to the accumulated plurality of frames of thedigitized radar return data and odometry data from the land vehicle togenerate transformed frames of data for each three-dimensional (x, y, z)point, wherein the RADON transform is configured to perform coherentintegration for each three-dimensional point for which a radar returnexists from the pulsed radar transmission, project a radar trajectoryonto each three-dimensional point, and project Doppler information ontoeach three-dimensional point; generating a two-dimensional X-Y map of anarea covered by the pulsed radar transmission from the SAR based on thetransformed frames of data for each three-dimensional point; andperforming an autonomous or semiautonomous maneuver with the landvehicle by applying the generated two-dimensional X-Y map.

In one embodiment, the RADON transform includes a range dimension, aDoppler dimension, and a phase dimension.

In one embodiment, the RADON transform is represented by:

${S\left( {x,y,z} \right)} = {\sum\limits_{f = 0}^{F - 1}{\sum\limits_{v = 0}^{V - 1}{\sum\limits_{h = 0}^{H - 1}{\sum\limits_{m = 0}^{M - 1}{\sum\limits_{n = 0}^{N - 1}{{s\left( {n,m,h,f} \right)}e^{{- 2}\pi j{R({m,f,x,y,z})}\frac{n}{N}}e^{{- 2}\pi j{D({m,f,x,y,z})}\frac{m}{M}}e^{{- 2}\pi j{P({m,h,v,f,x,y,z})}}}}}}}}$

wherein: R(m, f, x, y, z) represents a range dimension, D(m, f, x, y, z)represents a Doppler dimension, P(m, h, f, x, y, z) represents a phasedimension, m=sample index, n=chirp index, h=horizontal antenna index,v=vertical antenna index, f=frame index, x=x-axis location, y=y-axislocation, z=z-axis location, s=sampled signal, N=number of samples,M=number of chirps, H=number of horizontal antennas, V=number ofvertical antennas, and F=number of frames.

In one embodiment, the range dimension of the RADON transform isrepresented by:

${R\left( {m,f,x,y,z} \right)} = {\frac{2\alpha}{c}\sqrt{\left( {{O_{x}\left( {t\left( {m,f} \right)} \right)} - x} \right)^{2} + \left( {{O_{y}\left( {t\left( {m,f} \right)} \right)} - y} \right)^{2} + \left( {{O_{z}\left( {t\left( {m,f} \right)} \right)} - z} \right)^{2}}}$

wherein: c=speed of light, α=chirp slope, t(m, f)=mT_(c)+fT_(f),T_(c)=Chirp repetition interval, T_(f)=Frame repetition interval,O_(x)=Odometry based vehicle position at the x-axis, O_(y)=Odometrybased vehicle position at the y-axis, and O_(z)=Odometry based vehicleposition at the z-axis.

In one embodiment, the Doppler dimension of the RADON transform isrepresented by:

${D\left( {m,f,x,y,z} \right)} = {\frac{2}{\lambda}\frac{\begin{matrix}{{\left. {{O_{x}\left( {t\left( {m,f} \right)} \right)} - x} \right)O_{Vx}} +} \\{{\left( {{O_{y}\left( {t\left( {m,f} \right)} \right)} - y} \right)O_{Vy}} + {\left( {{O_{z}\left( {t\left( {m,f} \right)} \right)} - z} \right)O_{Vz}}}\end{matrix}}{\sqrt{\left( {{O_{x}\left( {t\left( {m,f} \right)} \right)} - x} \right)^{2} + \left( {{O_{y}\left( {t\left( {m,f} \right)} \right)} - y} \right)^{2} + \left( {{O_{z}\left( {t\left( {m,f} \right)} \right)} - z} \right)^{2}}}}$

wherein: t(m, f)=mT_(c)+fT_(f), λ=signal wavelength, T_(c)=Chirprepetition interval, T_(f)=Frame repetition interval, O_(x)=Odometrybased vehicle position at the x-axis, O_(y)=Odometry based vehicleposition at the y-axis, O_(z)=Odometry based vehicle position at thez-axis, O_(Vx)=Odometry based vehicle velocity at the x-axis,O_(Vy)=Odometry based vehicle velocity at the y-axis, andO_(Vz)=Odometry based vehicle velocity at the z-axis.

In one embodiment, the phase dimension of the RADON transform isrepresented by:

${P\left( {m,h,f,x,y,z} \right)} = {{\frac{\frac{\left. {{O_{y}\left( {t\left( {m,f} \right)} \right)} - y} \right)}{\left. {{O_{x}\left( {t\left( {m,f} \right)} \right)} - x} \right)}}{\begin{matrix}\sqrt{1 + \left( \frac{\left. {{O_{y}\left( {t\left( {mf} \right)} \right)} - y} \right)}{\left. {{O_{x}\left( {t\left( {mf} \right)} \right)} - x} \right)} \right)^{2}} \\\sqrt{1 + \frac{\left( {{O_{z}\left( {t\left( {mf} \right)} \right)} - z} \right)^{2}}{\left. {\left. \left( {{O_{x}\left( {t\left( {mf} \right)} \right)} - x} \right) \right)^{2} + \left( {{O_{y}\left( {t\left( {mf} \right)} \right)} - y} \right)} \right)^{2}}}\end{matrix}}h\frac{d_{h}}{\lambda}} + {\frac{\frac{{O_{z}\left( {t\left( {mf} \right)} \right)} - z}{\sqrt{\left. {\left. \left( {{O_{x}\left( {t\left( {mf} \right)} \right)} - x} \right) \right)^{2} + \left( {{O_{y}\left( {t\left( {mf} \right)} \right)} - y} \right)} \right)^{2}}}}{\sqrt{1 + \frac{\left( {{O_{z}\left( {t\left( {mf} \right)} \right)} - z} \right)^{2}}{\left. {\left. \left( {{O_{x}\left( {t\left( {mf} \right)} \right)} - x} \right) \right)^{2} + \left( {{O_{y}\left( {t\left( {mf} \right)} \right)} - y} \right)} \right)^{2}}}}v\frac{d_{v}}{\lambda}}}$

wherein: t(m, f)=mT_(c)+fT_(f), λ=signal wavelength, d_(h)=antennahorizontal spacing, d_(v)=antenna vertical spacing, T_(c)=Chirprepetition interval, T_(f)=Frame repetition interval, O_(x)=Odometrybased vehicle position at the x-axis, O_(y)=Odometry based vehicleposition at the y-axis, O_(z)=Odometry based vehicle position at thez-axis, O_(Vx)=Odometry based vehicle velocity at the x-axis,O_(Vy)=Odometry based vehicle velocity at the y-axis, andO_(Vz)=Odometry based vehicle velocity at the z-axis.

In one embodiment, the RADON transform is represented by:

${S\left( {x,y,z} \right)} = {\sum\limits_{f = 0}^{F - 1}{\sum\limits_{v = 0}^{V - 1}{\sum\limits_{h = 0}^{H - 1}{\sum\limits_{m = 0}^{M - 1}{\sum\limits_{n = 0}^{N - 1}{{s\left( {n,m,h,f} \right)}e^{{- 2}\pi j{R({m,f,x,y,z})}\frac{n}{N}}e^{{- 2}\pi j{D({m,f,x,y,z})}\frac{m}{M}}e^{{- 2}\pi j{P({m,h,v,f,x,y,z})}}}}}}}}$

wherein:

${R\left( {m,f,x,y,z} \right)} = {\frac{2\alpha}{c}\sqrt{\left( {{O_{x}\left( {t\left( {m,f} \right)} \right)} - x} \right)^{2} + \left( {{O_{y}\left( {t\left( {m,f} \right)} \right)} - y} \right)^{2} + \left( {{O_{z}\left( {t\left( {m,f} \right)} \right)} - z} \right)^{2}}}$${D\left( {m,f,x,y,z} \right)} = {\frac{2}{\lambda}\frac{\begin{matrix}{{\left. {{O_{x}\left( {t\left( {m,f} \right)} \right)} - x} \right)O_{Vx}} +} \\{{\left( {{O_{y}\left( {t\left( {m,f} \right)} \right)} - y} \right)O_{Vy}} + {\left( {{O_{z}\left( {t\left( {m,f} \right)} \right)} - z} \right)O_{Vz}}}\end{matrix}}{\sqrt{\left( {{O_{x}\left( {t\left( {m,f} \right)} \right)} - x} \right)^{2} + \left( {{O_{y}\left( {t\left( {m,f} \right)} \right)} - y} \right)^{2} + \left( {{O_{z}\left( {t\left( {m,f} \right)} \right)} - z} \right)^{2}}}}$${P\left( {m,h,f,x,y,z} \right)} = {{\frac{\frac{\left. {{O_{y}\left( {t\left( {m,f} \right)} \right)} - y} \right)}{\left. {{O_{x}\left( {t\left( {m,f} \right)} \right)} - x} \right)}}{\begin{matrix}\sqrt{1 + \left( \frac{\left. {{O_{y}\left( {t\left( {mf} \right)} \right)} - y} \right)}{\left. {{O_{x}\left( {t\left( {mf} \right)} \right)} - x} \right)} \right)^{2}} \\\sqrt{1 + \frac{\left( {{O_{z}\left( {t\left( {mf} \right)} \right)} - z} \right)^{2}}{\left. {\left. \left( {{O_{x}\left( {t\left( {mf} \right)} \right)} - x} \right) \right)^{2} + \left( {{O_{y}\left( {t\left( {mf} \right)} \right)} - y} \right)} \right)^{2}}}\end{matrix}}h\frac{d_{h}}{\lambda}} + {\frac{\frac{{O_{z}\left( {t\left( {mf} \right)} \right)} - z}{\sqrt{\left. {\left. \left( {{O_{x}\left( {t\left( {mf} \right)} \right)} - x} \right) \right)^{2} + \left( {{O_{y}\left( {t\left( {mf} \right)} \right)} - y} \right)} \right)^{2}}}}{\sqrt{1 + \frac{\left( {{O_{z}\left( {t\left( {mf} \right)} \right)} - z} \right)^{2}}{\left. {\left. \left( {{O_{x}\left( {t\left( {mf} \right)} \right)} - x} \right) \right)^{2} + \left( {{O_{y}\left( {t\left( {mf} \right)} \right)} - y} \right)} \right)^{2}}}}v\frac{d_{v}}{\lambda}}}$t(m, f) = mT_(c) + fT_(f)

m=sample index, n=chirp index, h=horizontal antenna index, v=verticalantenna index, f=frame index, x=x-axis location, y=y-axis location,z=z-axis location, s=sampled signal, N=number of samples, M=number ofchirps, H=number of horizontal antennas, V=number of vertical antennas,F=number of frames, c=speed of light, α=chirp slope, λ=signalwavelength, d_(h)=antenna horizontal spacing, d_(v)=antenna verticalspacing, T_(c)=Chirp repetition interval, T_(f)=Frame repetitioninterval, O_(x)=Odometry based vehicle position at the x-axis,O_(y)=Odometry based vehicle position at the y-axis, O_(z)=Odometrybased vehicle position at the z-axis, O_(Vx)=Odometry based vehiclevelocity at the x-axis, O_(Vy)=Odometry based vehicle velocity at they-axis, and O_(Vz)=Odometry based vehicle velocity at the z-axis.

BRIEF DESCRIPTION OF THE DRAWINGS

The exemplary embodiments will hereinafter be described in conjunctionwith the following drawing figures, wherein like numerals denote likeelements, and wherein:

FIG. 1 is a block diagram of an example vehicle that implementsSynthetic Aperture Radar, in accordance with various embodiments;

FIG. 2 is a process flow chart depicting an example process forprocessing radar returns from a SAR implemented on a vehicle to generatea map for use by the vehicle, in accordance with various embodiments;and

FIG. 3 is a process flow chart depicting an example process for usingSynthetic Aperture Radar (SAR) to perform a maneuver in a land vehicle,in accordance with various embodiments.

DETAILED DESCRIPTION

The following detailed description is merely exemplary in nature and isnot intended to limit the application and uses. Furthermore, there is nointention to be bound by any expressed or implied theory presented inthe preceding technical field, background, summary, or the followingdetailed description. As used herein, the term “module” refers to anyhardware, software, firmware, electronic control component, processinglogic, and/or processor device, individually or in any combination,including without limitation: application specific integrated circuit(ASIC), a field-programmable gate-array (FPGA), an electronic circuit, aprocessor (shared, dedicated, or group) and memory that executes one ormore software or firmware programs, a combinational logic circuit,and/or other suitable components that provide the describedfunctionality.

Embodiments of the present disclosure may be described herein in termsof functional and/or logical block components and various processingsteps. It should be appreciated that such block components may berealized by any number of hardware, software, and/or firmware componentsconfigured to perform the specified functions. For example, anembodiment of the present disclosure may employ various integratedcircuit components, e.g., memory elements, digital signal processingelements, logic elements, look-up tables, or the like, which may carryout a variety of functions under the control of one or moremicroprocessors or other control devices. In addition, those skilled inthe art will appreciate that embodiments of the present disclosure maybe practiced in conjunction with any number of systems, and that thesystems described herein is merely exemplary embodiments of the presentdisclosure.

For the sake of brevity, conventional techniques related to signalprocessing, data transmission, signaling, control, machine learningmodels, radar, lidar, image analysis, and other functional aspects ofthe systems (and the individual operating components of the systems) maynot be described in detail herein. Furthermore, the connecting linesshown in the various figures contained herein are intended to representexample functional relationships and/or physical couplings between thevarious elements. It should be noted that many alternative or additionalfunctional relationships or physical connections may be present in anembodiment of the present disclosure.

The subject matter described herein discloses apparatus, systems,techniques, and articles for adapting SAR for near field application inan automotive environment. The following disclosure provides examplesystems and methods for applying a novel SAR processing approach using aRadon transform. The described subject matter discloses apparatus,systems, techniques, and articles for accumulating multiple radar framesfrom a moving vehicle and projecting the gathered information accordingto the vehicle path to estimate the environment. In the describedsubject matter, a novel Radon-SAR transform is performed on theaccumulated data, coherently integrating multiple frames to generatehigh resolution detection.

In the described subject matter, in addition to the large spatialaperture generated from the vehicle movement, localization accuracy isincreased by exploiting Doppler information. In the described subjectmatter, the Doppler information reduces angular ambiguity, lowering theFPS requirement. The described apparatus, systems, techniques, andarticles adapt SAR for near field application by taking the vehicletrajectory into account. In the described subject matter, the adaptationto near field application is accomplished by projecting the vehicle pathto each position independently and calculating the Radon-SAR transformfor each projection. In the described subject matter, the near fieldenvironment increases accuracy and reduces ambiguity due to the multipleobservation projections. The described apparatus, systems, techniques,and articles can provide a two-dimensional X-Y map resulting from thedescribed process.

FIG. 1 depicts an example vehicle 100 that includes a SAR module 102 forusing Synthetic Aperture Radar (SAR) to assist the vehicle withperforming a maneuver. As depicted in FIG. 1, the vehicle 100 generallyincludes a chassis 12, a body 14, front wheels 16, and rear wheels 18.The body 14 is arranged on the chassis 12 and substantially enclosescomponents of the vehicle 100. The body 14 and the chassis 12 mayjointly form a frame. The wheels 16-18 are each rotationally coupled tothe chassis 12 near a respective corner of the body 14.

In various embodiments, the vehicle 100 may be an autonomous vehicle ora semi-autonomous vehicle. An autonomous vehicle 100 is, for example, avehicle that is automatically controlled to carry passengers from onelocation to another. The vehicle 100 is depicted in the illustratedembodiment as a passenger car, but other vehicle types, includingmotorcycles, trucks, sport utility vehicles (SUVs), recreationalvehicles (RVs), marine vessels, aircraft, etc., may also be used.

As shown, the vehicle 100 generally includes a propulsion system 20, atransmission system 22, a steering system 24, a brake system 26, asensor system 28, an actuator system 30, at least one data storagedevice 32, at least one controller 34, and a communication system 36.The propulsion system 20 may, in various embodiments, include aninternal combustion engine, an electric machine such as a tractionmotor, and/or a fuel cell propulsion system. The transmission system 22is configured to transmit power from the propulsion system 20 to thevehicle wheels 16 and 18 according to selectable speed ratios. Accordingto various embodiments, the transmission system 22 may include astep-ratio automatic transmission, a continuously-variable transmission,or other appropriate transmission.

The brake system 26 is configured to provide braking torque to thevehicle wheels 16 and 18. Brake system 26 may, in various embodiments,include friction brakes, brake by wire, a regenerative braking systemsuch as an electric machine, and/or other appropriate braking systems.

The steering system 24 influences a position of the vehicle wheels 16and/or 18. While depicted as including a steering wheel 25 forillustrative purposes, in some embodiments contemplated within the scopeof the present disclosure, the steering system 24 may not include asteering wheel.

The sensor system 28 includes one or more sensing devices 40 a-40 n thatsense observable conditions of the exterior environment and/or theinterior environment of the vehicle 100 (such as the state of one ormore occupants) and generate sensor data relating thereto. Sensingdevices 40 a-40 n might include, but are not limited to, radars (e.g.,long-range, medium-range-short range, SAR), lidars, global positioningsystems, optical cameras (e.g., forward facing, 360-degree, rear-facing,side-facing, stereo, etc.), thermal (e.g., infrared) cameras, ultrasonicsensors, odometry sensors (e.g., encoders) and/or other sensors thatmight be utilized in connection with systems and methods in accordancewith the present subject matter.

The actuator system 30 includes one or more actuator devices 42 a-42 nthat control one or more vehicle features such as, but not limited to,the propulsion system 20, the transmission system 22, the steeringsystem 24, and the brake system 26. In various embodiments, vehicle 100may also include interior and/or exterior vehicle features notillustrated in FIG. 1, such as various doors, a trunk, and cabinfeatures such as air, music, lighting, touch-screen display components(such as those used in connection with navigation systems), and thelike.

The data storage device 32 stores data for use in automaticallycontrolling the vehicle 100. The data storage device 32 may be part ofthe controller 34, separate from the controller 34, or part of thecontroller 34 and part of a separate system. In various embodiments,controller 34 implements a SAR module 102 that is configured toimplement SAR processing.

The controller 34 includes at least one processor 44 and acomputer-readable storage device or media 46. The processor 44 may beany custom-made or commercially available processor, a centralprocessing unit (CPU), a graphics processing unit (GPU), an applicationspecific integrated circuit (ASIC) (e.g., a custom ASIC implementing aneural network), a field programmable gate array (FPGA), an auxiliaryprocessor among several processors associated with the controller 34, asemiconductor-based microprocessor (in the form of a microchip or chipset), any combination thereof, or generally any device for executinginstructions. The computer readable storage device or media 46 mayinclude volatile and nonvolatile storage in read-only memory (ROM),random-access memory (RAM), and keep-alive memory (KAM), for example.KAM is a persistent or non-volatile memory that may be used to storevarious operating variables while the processor 44 is powered down. Thecomputer-readable storage device or media 46 may be implemented usingany of a number of known memory devices such as PROMs (programmableread-only memory), EPROMs (electrically PROM), EEPROMs (electricallyerasable PROM), flash memory, or any other electric, magnetic, optical,or combination memory devices capable of storing data, some of whichrepresent executable instructions, used by the controller 34 incontrolling the vehicle 100.

The instructions may include one or more separate programs, each ofwhich comprises an ordered listing of executable instructions forimplementing logical functions. The instructions, when executed by theprocessor 44, receive and process signals (e.g., sensor data) from thesensor system 28, perform logic, calculations, methods and/or algorithmsfor automatically controlling the components of the vehicle 100, andgenerate control signals that are transmitted to the actuator system 30to automatically control the components of the vehicle 100 based on thelogic, calculations, methods, and/or algorithms. Although only onecontroller 34 is shown in FIG. 1, embodiments of the vehicle 100 mayinclude any number of controllers 34 that communicate over any suitablecommunication medium or a combination of communication mediums and thatcooperate to process the sensor signals, perform logic, calculations,methods, and/or algorithms, and generate control signals toautomatically control features of the vehicle 100.

FIG. 2 is a process flow chart depicting an example process 200 forprocessing radar returns (e.g., by SAR module 102 implemented bycontroller 34) from a SAR (e.g., from a sensor system 28 that includesone or more sensing devices 40 a-40 n that implements SAR) implementedon a vehicle (e.g., vehicle 100) to generate a map for use by thevehicle. The order of operation within process 200 is not limited to thesequential execution as illustrated in the FIG. 2 but may be performedin one or more varying orders as applicable and in accordance with thepresent disclosure.

The example process 200 includes performing analog to digital conversion(ADC) on radar returns from a SAR in the vehicle (operation 302) toproduce a frame of digital data for each converted radar return. The ADCmay be performed using conventional methods used in radar systems in avehicle.

The example process 200 includes accumulating multiple frames of thedigitized data (operation 204). Each frame may include radar data fromthe return for a specific three-dimensional location identified by x, y,z coordinates (hereinafter referred to as (x, y, z) location) gatheredfrom a pulsed transmission. The x, y, z coordinates are based on acoordinate system with an x-axis direction in the direction of vehicletravel, a y-axis direction that is 90 degrees to the left of the x-axis,and a z-axis direction that is 90 degrees in a vertical direction tovehicle travel. The multiple frames may include all or almost all theframes of data gathered from a pulsed transmission.

The example process 200 includes processing the accumulated frames ofthe digitized data using a RADON-SAR transform (operation 206) andvehicle odometry data 207. The vehicle odometry data may include vehicleposition and velocity data. The RADON-SAR transform is a type of Radontransform that has been specially adapted for use with SAR. TheRADON-SAR transform is configured to perform coherent integration forevery (x, y, z) point (e.g., (x, y, z) location for which a radar returnexists from the pulsed transmission). The RADON-SAR transform isconfigured to account for a radar trajectory, according to the vehiclepath, by projecting the radar trajectory onto each three-dimensional (x,y, z) point and coherently integrate the accumulated frames. This allowsthe SAR to support arbitrary radar trajectory, in addition to straightline trajectory with a constant velocity. The RADON-SAR transform isconfigured to account for Doppler information to increase accuracy andreduce ambiguity. The RADON-SAR transform includes a range dimension, aDoppler dimension, and a phase dimension. This configures the RADON-SARtransform to support range, Doppler, and spatial migration within framesand between of frames, caused from radar movement. The example RADON-SARtransform assumes static objects. The coherent integration performed inthe RADON-SAR transform increase target signal-to-noise-ratio (SNR).

An example RADON-SAR transform is represented by:

${S\left( {x,y,z} \right)} = {\sum\limits_{f = 0}^{F - 1}{\sum\limits_{v = 0}^{V - 1}{\sum\limits_{h = 0}^{H - 1}{\sum\limits_{m = 0}^{M - 1}{\sum\limits_{n = 0}^{N - 1}{{s\left( {n,m,h,f} \right)}e^{{- 2}\pi j{R({m,f,x,y,z})}\frac{n}{N}}e^{{- 2}\pi j{D({m,f,x,y,z})}\frac{m}{M}}e^{{- 2}\pi j{P({m,h,v,f,x,y,z})}}}}}}}}$

where:

${R\left( {m,f,x,y,z} \right)} = {\frac{2\alpha}{c}\sqrt{\left( {{O_{x}\left( {t\left( {m,f} \right)} \right)} - x} \right)^{2} + \left( {{O_{y}\left( {t\left( {m,f} \right)} \right)} - y} \right)^{2} + \left( {{O_{z}\left( {t\left( {m,f} \right)} \right)} - z} \right)^{2}}}$${D\left( {m,f,x,y,z} \right)} = {\frac{2}{\lambda}\frac{\begin{matrix}{{\left. {{O_{x}\left( {t\left( {m,f} \right)} \right)} - x} \right)O_{Vx}} +} \\{{\left( {{O_{y}\left( {t\left( {m,f} \right)} \right)} - y} \right)O_{Vy}} + {\left( {{O_{z}\left( {t\left( {m,f} \right)} \right)} - z} \right)O_{Vz}}}\end{matrix}}{\sqrt{\left( {{O_{x}\left( {t\left( {m,f} \right)} \right)} - x} \right)^{2} + \left( {{O_{y}\left( {t\left( {m,f} \right)} \right)} - y} \right)^{2} + \left( {{O_{z}\left( {t\left( {m,f} \right)} \right)} - z} \right)^{2}}}}$${P\left( {m,h,f,x,y,z} \right)} = {{\frac{\frac{\left. {{O_{y}\left( {t\left( {m,f} \right)} \right)} - y} \right)}{\left. {{O_{x}\left( {t\left( {m,f} \right)} \right)} - x} \right)}}{\begin{matrix}\sqrt{1 + \left( \frac{\left. {{O_{y}\left( {t\left( {mf} \right)} \right)} - y} \right)}{\left. {{O_{x}\left( {t\left( {mf} \right)} \right)} - x} \right)} \right)^{2}} \\\sqrt{1 + \frac{\left( {{O_{z}\left( {t\left( {mf} \right)} \right)} - z} \right)^{2}}{\left. {\left. \left( {{O_{x}\left( {t\left( {mf} \right)} \right)} - x} \right) \right)^{2} + \left( {{O_{y}\left( {t\left( {mf} \right)} \right)} - y} \right)} \right)^{2}}}\end{matrix}}h\frac{d_{h}}{\lambda}} + {\frac{\frac{{O_{z}\left( {t\left( {mf} \right)} \right)} - z}{\sqrt{\left. {\left. \left( {{O_{x}\left( {t\left( {mf} \right)} \right)} - x} \right) \right)^{2} + \left( {{O_{y}\left( {t\left( {mf} \right)} \right)} - y} \right)} \right)^{2}}}}{\sqrt{1 + \frac{\left( {{O_{z}\left( {t\left( {mf} \right)} \right)} - z} \right)^{2}}{\left. {\left. \left( {{O_{x}\left( {t\left( {mf} \right)} \right)} - x} \right) \right)^{2} + \left( {{O_{y}\left( {t\left( {mf} \right)} \right)} - y} \right)} \right)^{2}}}}v\frac{d_{v}}{\lambda}}}$t(m, f) = mT_(c) + fT_(f)

-   m—sample index-   n—chirp index-   h—horizontal antenna index-   v—vertical antenna index-   f—frame index-   x—x-axis location-   y—y-axis location-   z—z-axis location-   s—sampled signal-   c—speed of light-   N—number of samples-   M—number of chirps-   H—number of horizontal antennas-   V—number of vertical antennas-   F—number of frames-   α—chirp slope-   λ—signal wavelength-   d_(h)—antenna horizontal spacing-   d_(v)antenna vertical spacing-   T_(c)Chirp repetition interval-   T_(f)—Frame repetition interval-   O_(x)—Odometry based vehicle position at the x-axis-   O_(y)—Odometry based vehicle position at the y-axis-   O_(z)—Odometry based vehicle position at the z-axis-   O_(Vx)—Odometry based vehicle velocity at the x-axis-   O_(Vy)—Odometry based vehicle velocity at the y-axis-   O_(Vz)—Odometry based vehicle velocity at the z-axis

The example process 200 includes generating a two-dimensional X-Y map ofthe area covered by the pulsed radar transmission from the SAR based onthe transformed frames of data for each three-dimensional (x, y, z)point (operation 208). The two-dimensional X-Y map may be generatedusing conventional techniques for generating a map from radar returndata.

After generation of a two-dimensional X-Y map, the vehicle may use thedata from the two-dimensional X-Y map for autonomous or semi-autonomousdriving features such as parking spot detection for automatic parkassist. The increased resolution provided by use of SAR and theRADON-SAR transform can improve a vehicle's ability to maneuver intosmaller parking spaces because the boundaries of a parking space will beknown with greater detail.

FIG. 3 is a process flow chart depicting an example process 300 forusing Synthetic Aperture Radar (SAR) to perform a maneuver in a landvehicle (e.g., vehicle 100). The example process 300 includes receivingdigitized radar return data (e.g., from a sensor system 28 that includesone or more sensing devices 40 a-40 n that implements SAR) from a pulsedradar transmission from a SAR onboard the land vehicle (operation 302)and accumulating a plurality of frames of the digitized radar returndata (operation 304).

The example process 300 includes applying a RADON transform (e.g., bySAR module 102 implemented by controller 34) to the accumulatedplurality of frames of the digitized radar return data and odometry datafrom the land vehicle to generate transformed frames of data for eachthree-dimensional point (operation 306). The RADON transform isconfigured to perform coherent integration for each three-dimensionalpoint for which a radar return exists from the pulsed radartransmission, project a radar trajectory onto each three-dimensionalpoint, and project Doppler information onto each three-dimensionalpoint. The example RADON-SAR transform presented above may be used asthe RADON transform.

The example process 300 includes generating a two-dimensional X-Y map ofan area covered by the pulsed radar transmission from the SAR based onthe transformed frames of data for each three-dimensional point(operation 308) and performing an autonomous or semiautonomous maneuverwith the land vehicle by applying the generated two-dimensional X-Y map(operation 310). The two-dimensional X-Y map may be generated usingconventional techniques for generating a map from radar return data. Theautonomous or semiautonomous maneuver may include a parking assistmaneuver or some other maneuver that could benefit from highly accurateposition data that can be provided from SAR.

The foregoing outlines features of several embodiments so that thoseskilled in the art may better understand the aspects of the presentdisclosure. Those skilled in the art should appreciate that they mayreadily use the present disclosure as a basis for designing or modifyingother processes and structures for carrying out the same purposes and/orachieving the same advantages of the embodiments introduced herein.Those skilled in the art should also realize that such equivalentconstructions do not depart from the spirit and scope of the presentdisclosure, and that they may make various changes, substitutions, andalterations herein without departing from the spirit and scope of thepresent disclosure.

What is claimed is:
 1. A method for using Synthetic Aperture Radar (SAR)to perform a maneuver in a land vehicle, the method comprising:receiving digitized radar return data from a pulsed radar transmissionfrom a Synthetic Aperture Radar (SAR) onboard a land vehicle;accumulating a plurality of frames of the digitized radar return data;applying a RADON transform to the accumulated plurality of frames of thedigitized radar return data and odometry data from the land vehicle togenerate transformed frames of data for each three-dimensional point,wherein the RADON transform is configured to perform coherentintegration for each three-dimensional point for which a radar returnexists from the pulsed radar transmission, project a radar trajectoryonto each three-dimensional point, and project Doppler information ontoeach three-dimensional point; generating a two-dimensional X-Y map of anarea covered by the pulsed radar transmission from the SAR based on thetransformed frames of data for each three-dimensional point; andperforming an autonomous or semiautonomous maneuver with the landvehicle by applying the generated two-dimensional X-Y map.
 2. The methodof claim 1, wherein the RADON transform comprises a range dimension, aDoppler dimension, and a phase dimension.
 3. The method of claim 2,wherein the RADON transform is represented by:${S\left( {x,y,z} \right)} = {\sum\limits_{f = 0}^{F - 1}{\sum\limits_{v = 0}^{V - 1}{\sum\limits_{h = 0}^{H - 1}{\sum\limits_{m = 0}^{M - 1}{\sum\limits_{n = 0}^{N - 1}{{s\left( {n,m,h,f} \right)}e^{{- 2}\pi j{R({m,f,x,y,z})}\frac{n}{N}}e^{{- 2}\pi j{D({m,f,x,y,z})}\frac{m}{M}}e^{{- 2}\pi j{P({m,h,v,f,x,y,z})}}}}}}}}$wherein: R(m, f, x, y, z) represents the range dimension, D(m, f, x, y,z) represents the Doppler dimension, P(m, h, f, x, y, z) represents thephase dimension, m=sample index, n=chirp index, h=horizontal antennaindex, v=vertical antenna index, f=frame index, x=x-axis location,y=y-axis location, z=z-axis location, s=sampled signal, N=number ofsamples, M=number of chirps, H=number of horizontal antennas, V=numberof vertical antennas, and F=number of frames.
 4. The method of claim 3,wherein the range dimension of the RADON transform is represented by:${R\left( {m,f,x,y,z} \right)} = {\frac{2\alpha}{c}\sqrt{\left( {{O_{x}\left( {t\left( {m,f} \right)} \right)} - x} \right)^{2} + \left( {{O_{y}\left( {t\left( {m,f} \right)} \right)} - y} \right)^{2} + \left( {{O_{z}\left( {t\left( {m,f} \right)} \right)} - z} \right)^{2}}}$wherein: c=speed of light, α=chirp slope, t(m, f)=mT_(c)+fT_(f),T_(c)=Chirp repetition interval, T_(f)=Frame repetition interval,O_(x)=Odometry based vehicle position at the x-axis, O_(y)=Odometrybased vehicle position at the y-axis, and O_(z)=Odometry based vehicleposition at the z-axis.
 5. The method of claim 3, wherein the Dopplerdimension of the RADON transform is represented by:${D\left( {m,f,x,y,z} \right)} = {\frac{2}{\lambda}\frac{\begin{matrix}{{\left. {{O_{x}\left( {t\left( {m,f} \right)} \right)} - x} \right)O_{Vx}} +} \\{{\left( {{O_{y}\left( {t\left( {m,f} \right)} \right)} - y} \right)O_{Vy}} + {\left( {{O_{z}\left( {t\left( {m,f} \right)} \right)} - z} \right)O_{Vz}}}\end{matrix}}{\sqrt{\left( {{O_{x}\left( {t\left( {m,f} \right)} \right)} - x} \right)^{2} + \left( {{O_{y}\left( {t\left( {m,f} \right)} \right)} - y} \right)^{2} + \left( {{O_{z}\left( {t\left( {m,f} \right)} \right)} - z} \right)^{2}}}}$wherein: t(m, f)=mT_(c)+fT_(f), λ=signal wavelength, T_(c)=Chirprepetition interval, T_(f)=Frame repetition interval, O_(x)=Odometrybased vehicle position at the x-axis, O_(y)=Odometry based vehicleposition at the y-axis, O_(z)=Odometry based vehicle position at thez-axis, O_(Vx)=Odometry based vehicle velocity at the x-axis,O_(Vy)=Odometry based vehicle velocity at the y-axis, andO_(Vz)=Odometry based vehicle velocity at the z-axis.
 6. The method ofclaim 3, wherein the phase dimension of the RADON transform isrepresented by:${P\left( {m,h,f,x,y,z} \right)} = {{\frac{\frac{\left. {{O_{y}\left( {t\left( {m,f} \right)} \right)} - y} \right)}{\left. {{O_{x}\left( {t\left( {m,f} \right)} \right)} - x} \right)}}{\begin{matrix}\sqrt{1 + \left( \frac{\left. {{O_{y}\left( {t\left( {m,f} \right)} \right)} - y} \right)}{\left. {{O_{x}\left( {t\left( {m,f} \right)} \right)} - x} \right)} \right)^{2}} \\\sqrt{1 + \frac{\left( {{O_{z}\left( {t\left( {m,f} \right)} \right)} - z} \right)^{2}}{\left( {{O_{x}\left( {t\left( {m,f} \right)} \right)} - x} \right)^{2} + \left( {{O_{y}\left( {t\left( {m,f} \right)} \right)} - y} \right)^{2}}}\end{matrix}}h\frac{d_{h}}{\lambda}} + {\frac{\frac{{O_{z}\left( {t\left( {m,f} \right)} \right)} - z}{\sqrt{\left. {\left. \left( {{O_{x}\left( {t\left( {m,f} \right)} \right)} - x} \right) \right)^{2} + \left( {{O_{y}\left( {t\left( {m,f} \right)} \right)} - y} \right)} \right)^{2}}}}{\sqrt{1 + \frac{\left( {{O_{z}\left( {t\left( {m,f} \right)} \right)} - z} \right)^{2}}{\left. {\left. \left( {{O_{x}\left( {t\left( {m,f} \right)} \right)} - x} \right) \right)^{2} + \left( {{O_{y}\left( {t\left( {m,f} \right)} \right)} - y} \right)} \right)^{2}}}}v\frac{d_{v}}{\lambda}}}$wherein: t(m, f)=mT_(c)+fT_(f), λ=signal wavelength, d_(h)=antennahorizontal spacing, d_(v)=antenna vertical spacing, T_(c)=Chirprepetition interval, T_(f)=Frame repetition interval, O_(x)=Odometrybased vehicle position at the x-axis, O_(y)=Odometry based vehicleposition at the y-axis, O_(z)=Odometry based vehicle position at thez-axis, O_(Vx)=Odometry based vehicle velocity at the x-axis,O_(Vy)=Odometry based vehicle velocity at the y-axis, andO_(Vz)=Odometry based vehicle velocity at the z-axis.
 7. The method ofclaim 1, wherein the RADON transform is represented by:${S\left( {x,y,z} \right)} = {\sum\limits_{f = 0}^{F - 1}{\sum\limits_{v = 0}^{V - 1}{\sum\limits_{h = 0}^{H - 1}{\sum\limits_{m = 0}^{M - 1}{\sum\limits_{n = 0}^{N - 1}{{s\left( {n,m,h,f} \right)}e^{{- 2}\pi j{R({m,f,x,y,z})}\frac{n}{N}}e^{{- 2}\pi j{D({m,f,x,y,z})}\frac{m}{M}}e^{{- 2}\pi j{P({m,h,v,f,x,y,z})}}}}}}}}$wherein:${R\left( {m,f,x,y,z} \right)} = {\frac{2\alpha}{c}\sqrt{\left( {{O_{x}\left( {t\left( {m,f} \right)} \right)} - x} \right)^{2} + \left( {{O_{y}\left( {t\left( {m,f} \right)} \right)} - y} \right)^{2} + \left( {{O_{z}\left( {t\left( {m,f} \right)} \right)} - z} \right)^{2}}}$${D\left( {m,f,x,y,z} \right)} = {\frac{2}{\lambda}\frac{\begin{matrix}{{\left. {{O_{x}\left( {t\left( {m,f} \right)} \right)} - x} \right)O_{Vx}} +} \\{{\left( {{O_{y}\left( {t\left( {m,f} \right)} \right)} - y} \right)O_{Vy}} + {\left( {{O_{z}\left( {t\left( {m,f} \right)} \right)} - z} \right)O_{Vz}}}\end{matrix}}{\sqrt{\left( {{O_{x}\left( {t\left( {m,f} \right)} \right)} - x} \right)^{2} + \left( {{O_{y}\left( {t\left( {m,f} \right)} \right)} - y} \right)^{2} + \left( {{O_{z}\left( {t\left( {m,f} \right)} \right)} - z} \right)^{2}}}}$${P\left( {m,h,f,x,y,z} \right)} = {{\frac{\frac{\left. {{O_{y}\left( {t\left( {m,f} \right)} \right)} - y} \right)}{\left. {{O_{x}\left( {t\left( {m,f} \right)} \right)} - x} \right)}}{\begin{matrix}\sqrt{1 + \left( \frac{\left. {{O_{y}\left( {t\left( {m,f} \right)} \right)} - y} \right)}{\left. {{O_{x}\left( {t\left( {m,f} \right)} \right)} - x} \right)} \right)^{2}} \\\sqrt{1 + \frac{\left( {{O_{z}\left( {t\left( {m,f} \right)} \right)} - z} \right)^{2}}{\left( {{O_{x}\left( {t\left( {m,f} \right)} \right)} - x} \right)^{2} + \left( {{O_{y}\left( {t\left( {m,f} \right)} \right)} - y} \right)^{2}}}\end{matrix}}h\frac{d_{h}}{\lambda}} + {\frac{\frac{{O_{z}\left( {t\left( {m,f} \right)} \right)} - z}{\sqrt{\left. {\left. \left( {{O_{x}\left( {t\left( {m,f} \right)} \right)} - x} \right) \right)^{2} + \left( {{O_{y}\left( {t\left( {m,f} \right)} \right)} - y} \right)} \right)^{2}}}}{\sqrt{1 + \frac{\left( {{O_{z}\left( {t\left( {m,f} \right)} \right)} - z} \right)^{2}}{\left. {\left. \left( {{O_{x}\left( {t\left( {m,f} \right)} \right)} - x} \right) \right)^{2} + \left( {{O_{y}\left( {t\left( {m,f} \right)} \right)} - y} \right)} \right)^{2}}}}v\frac{d_{v}}{\lambda}}}$t(m, f) = mT_(c) + fT_(f) m=sample index, n=chirp index, h=horizontalantenna index, v=vertical antenna index, f=frame index, x=x-axislocation, y=y-axis location, z=z-axis location, s=sampled signal,N=number of samples, M=number of chirps, H=number of horizontalantennas, V=number of vertical antennas, F=number of frames, c=speed oflight, α=chirp slope, λ=signal wavelength, d_(h)=antenna horizontalspacing, d_(v)=antenna vertical spacing, T_(c)=Chirp repetitioninterval, T_(f)=Frame repetition interval, O_(x)=Odometry based vehicleposition at the x-axis, O_(y)=Odometry based vehicle position at they-axis, O_(z)=Odometry based vehicle position at the z-axis,O_(Vx)=Odometry based vehicle velocity at the x-axis, O_(Vy)=Odometrybased vehicle velocity at the y-axis, and O_(Vz)=Odometry based vehiclevelocity at the z-axis.
 8. A system for applying Synthetic ApertureRadar (SAR) in a land vehicle to perform a maneuver, the systemcomprising a controller configured to: receive digitized radar returndata from a pulsed radar transmission from a Synthetic Aperture Radar(SAR) onboard a land vehicle; accumulate a plurality of frames of thedigitized radar return data; apply a RADON transform to the accumulatedplurality of frames of the digitized radar return data and odometry datafrom the land vehicle to generate transformed frames of data for eachthree-dimensional point, wherein the RADON transform is configured toperform coherent integration for each three-dimensional point for whicha radar return exists from the pulsed radar transmission, project aradar trajectory onto each three-dimensional point, and project Dopplerinformation onto each three-dimensional point; generate atwo-dimensional X-Y map of an area covered by the pulsed radartransmission from the SAR based on the transformed frames of data foreach three-dimensional point; and perform an autonomous orsemiautonomous maneuver with the land vehicle by applying the generatedtwo-dimensional X-Y map.
 9. The system of claim 8, wherein the RADONtransform comprises a range dimension, a Doppler dimension, and a phasedimension.
 10. The system of claim 9, wherein the RADON transform isrepresented by:${S\left( {x,y,z} \right)} = {\sum\limits_{f = 0}^{F - 1}{\sum\limits_{v = 0}^{V - 1}{\sum\limits_{h = 0}^{H - 1}{\sum\limits_{m = 0}^{M - 1}{\sum\limits_{n = 0}^{N - 1}{{s\left( {n,m,h,f} \right)}e^{{- 2}\pi j{R({m,f,x,y,z})}\frac{n}{N}}e^{{- 2}\pi j{D({m,f,x,y,z})}\frac{m}{M}}e^{{- 2}\pi j{P({m,h,v,f,x,y,z})}}}}}}}}$wherein: R(m, f, x, y, z) represents the range dimension, D(m, f, x, y,z) represents the Doppler dimension, P(m, h, f, x, y, z) represents thephase dimension, m=sample index, n=chirp index, h=horizontal antennaindex, v=vertical antenna index, f=frame index, x=x-axis location,y=y-axis location, z=z-axis location, s=sampled signal, N=number ofsamples, M=number of chirps, H=number of horizontal antennas, V=numberof vertical antennas, and F=number of frames.
 11. The system of claim10, wherein the range dimension of the RADON transform is representedby:${R\left( {m,f,x,y,z} \right)} = {\frac{2\alpha}{c}\sqrt{\left( {{O_{x}\left( {t\left( {m,f} \right)} \right)} - x} \right)^{2} + \left( {{O_{y}\left( {t\left( {m,f} \right)} \right)} - y} \right)^{2} + \left( {{O_{z}\left( {t\left( {m,f} \right)} \right)} - z} \right)^{2}}}$wherein: c=speed of light, α=chirp slope, t(m, f)=mT_(c)+fT_(f),T_(c)=Chirp repetition interval, T_(f)=Frame repetition interval,O_(x)=Odometry based vehicle position at the x-axis, O_(y)=Odometrybased vehicle position at the y-axis, and O_(z)=Odometry based vehicleposition at the z-axis.
 12. The system of claim 10, wherein the Dopplerdimension of the RADON transform is represented by:${D\left( {m,f,x,y,z} \right)} = {\frac{2}{\lambda}\frac{\begin{matrix}{{\left. {{O_{x}\left( {t\left( {m,f} \right)} \right)} - x} \right)O_{Vx}} +} \\{{\left( {{O_{y}\left( {t\left( {m,f} \right)} \right)} - y} \right)O_{Vy}} + {\left( {{O_{z}\left( {t\left( {m,f} \right)} \right)} - z} \right)O_{Vz}}}\end{matrix}}{\sqrt{\left( {{O_{x}\left( {t\left( {m,f} \right)} \right)} - x} \right)^{2} + \left( {{O_{y}\left( {t\left( {m,f} \right)} \right)} - y} \right)^{2} + \left( {{O_{z}\left( {t\left( {m,f} \right)} \right)} - z} \right)^{2}}}}$wherein: t(m, f)=mT_(c)+fT_(f), λ=signal wavelength, T_(c)=Chirprepetition interval, T_(f)=Frame repetition interval, O_(x)=Odometrybased vehicle position at the x-axis, O_(y)=Odometry based vehicleposition at the y-axis, O_(z)=Odometry based vehicle position at thez-axis, O_(Vx)=Odometry based vehicle velocity at the x-axis,O_(Vy)=Odometry based vehicle velocity at the y-axis, andO_(Vz)=Odometry based vehicle velocity at the z-axis.
 13. The system ofclaim 10, wherein the phase dimension of the RADON transform isrepresented by:${P\left( {m,h,f,x,y,z} \right)} = {{\frac{\frac{\left. {{O_{y}\left( {t\left( {m,f} \right)} \right)} - y} \right)}{\left. {{O_{x}\left( {t\left( {m,f} \right)} \right)} - x} \right)}}{\begin{matrix}\sqrt{1 + \left( \frac{\left. {{O_{y}\left( {t\left( {m,f} \right)} \right)} - y} \right)}{\left. {{O_{x}\left( {t\left( {m,f} \right)} \right)} - x} \right)} \right)^{2}} \\\sqrt{1 + \frac{\left( {{O_{z}\left( {t\left( {m,f} \right)} \right)} - z} \right)^{2}}{\left( {{O_{x}\left( {t\left( {m,f} \right)} \right)} - x} \right)^{2} + \left( {{O_{y}\left( {t\left( {m,f} \right)} \right)} - y} \right)^{2}}}\end{matrix}}h\frac{d_{h}}{\lambda}} + {\frac{\frac{{O_{z}\left( {t\left( {m,f} \right)} \right)} - z}{\sqrt{\left. {\left. \left( {{O_{x}\left( {t\left( {m,f} \right)} \right)} - x} \right) \right)^{2} + \left( {{O_{y}\left( {t\left( {m,f} \right)} \right)} - y} \right)} \right)^{2}}}}{\sqrt{1 + \frac{\left( {{O_{z}\left( {t\left( {m,f} \right)} \right)} - z} \right)^{2}}{\left. {\left. \left( {{O_{x}\left( {t\left( {m,f} \right)} \right)} - x} \right) \right)^{2} + \left( {{O_{y}\left( {t\left( {m,f} \right)} \right)} - y} \right)} \right)^{2}}}}v\frac{d_{v}}{\lambda}}}$wherein: t(m, f)=mT_(c)+fT_(f), λ=signal wavelength, d_(h)=antennahorizontal spacing, d_(v)=antenna vertical spacing, T_(c)=Chirprepetition interval, T_(f)=Frame repetition interval, O_(x)=Odometrybased vehicle position at the x-axis, O_(y)=Odometry based vehicleposition at the y-axis, O_(z)=Odometry based vehicle position at thez-axis, O_(Vx)=Odometry based vehicle velocity at the x-axis,O_(Vy)=Odometry based vehicle velocity at the y-axis, andO_(Vz)=Odometry based vehicle velocity at the z-axis.
 14. The system ofclaim 8, wherein the RADON transform is represented by:${S\left( {x,y,z} \right)} = {\sum\limits_{f = 0}^{F - 1}{\sum\limits_{v = 0}^{V - 1}{\sum\limits_{h = 0}^{H - 1}{\sum\limits_{m = 0}^{M - 1}{\sum\limits_{n = 0}^{N - 1}{{s\left( {n,m,h,f} \right)}e^{{- 2}\pi j{R({m,f,x,y,z})}\frac{n}{N}}e^{{- 2}\pi j{D({m,f,x,y,z})}\frac{m}{M}}e^{{- 2}\pi j{P({m,h,v,f,x,y,z})}}}}}}}}$wherein:${R\left( {m,f,x,y,z} \right)} = {\frac{2\alpha}{c}\sqrt{\left( {{O_{x}\left( {t\left( {m,f} \right)} \right)} - x} \right)^{2} + \left( {{O_{y}\left( {t\left( {m,f} \right)} \right)} - y} \right)^{2} + \left( {{O_{z}\left( {t\left( {m,f} \right)} \right)} - z} \right)^{2}}}$${D\left( {m,f,x,y,z} \right)} = {\frac{2}{\lambda}\frac{\begin{matrix}{{\left. {{O_{x}\left( {t\left( {m,f} \right)} \right)} - x} \right)O_{Vx}} +} \\{{\left( {{O_{y}\left( {t\left( {m,f} \right)} \right)} - y} \right)O_{Vy}} + {\left( {{O_{z}\left( {t\left( {m,f} \right)} \right)} - z} \right)O_{Vz}}}\end{matrix}}{\sqrt{\left( {{O_{x}\left( {t\left( {m,f} \right)} \right)} - x} \right)^{2} + \left( {{O_{y}\left( {t\left( {m,f} \right)} \right)} - y} \right)^{2} + \left( {{O_{z}\left( {t\left( {m,f} \right)} \right)} - z} \right)^{2}}}}$${P\left( {m,h,f,x,y,z} \right)} = {{\frac{\frac{\left. {{O_{y}\left( {t\left( {m,f} \right)} \right)} - y} \right)}{\left. {{O_{x}\left( {t\left( {m,f} \right)} \right)} - x} \right)}}{\begin{matrix}\sqrt{1 + \left( \frac{\left. {{O_{y}\left( {t\left( {m,f} \right)} \right)} - y} \right)}{\left. {{O_{x}\left( {t\left( {m,f} \right)} \right)} - x} \right)} \right)^{2}} \\\sqrt{1 + \frac{\left( {{O_{z}\left( {t\left( {m,f} \right)} \right)} - z} \right)^{2}}{\left( {{O_{x}\left( {t\left( {m,f} \right)} \right)} - x} \right)^{2} + \left( {{O_{y}\left( {t\left( {m,f} \right)} \right)} - y} \right)^{2}}}\end{matrix}}h\frac{d_{h}}{\lambda}} + {\frac{\frac{{O_{z}\left( {t\left( {m,f} \right)} \right)} - z}{\sqrt{\left. {\left. \left( {{O_{x}\left( {t\left( {m,f} \right)} \right)} - x} \right) \right)^{2} + \left( {{O_{y}\left( {t\left( {m,f} \right)} \right)} - y} \right)} \right)^{2}}}}{\sqrt{1 + \frac{\left( {{O_{z}\left( {t\left( {m,f} \right)} \right)} - z} \right)^{2}}{\left. {\left. \left( {{O_{x}\left( {t\left( {m,f} \right)} \right)} - x} \right) \right)^{2} + \left( {{O_{y}\left( {t\left( {m,f} \right)} \right)} - y} \right)} \right)^{2}}}}v\frac{d_{v}}{\lambda}}}$t(m, f) = mT_(c) + fT_(f) m=sample index, n=chirp index, h=horizontalantenna index, v=vertical antenna index, f=frame index, x=x-axislocation, y=y-axis location, z=z-axis location, s=sampled signal,N=number of samples, M=number of chirps, H=number of horizontalantennas, V=number of vertical antennas, F=number of frames, c=speed oflight, α=chirp slope, λ=signal wavelength, d_(h)=antenna horizontalspacing, d_(v)=antenna vertical spacing, T_(c)=Chirp repetitioninterval, T_(f)=Frame repetition interval, O_(x)=Odometry based vehicleposition at the x-axis, O_(y)=Odometry based vehicle position at they-axis, O_(z)=Odometry based vehicle position at the z-axis,O_(Vx)=Odometry based vehicle velocity at the x-axis, O_(Vy)=Odometrybased vehicle velocity at the y-axis, and O_(Vz)=Odometry based vehiclevelocity at the z-axis.
 15. A non-transitory computer readable mediaencoded with programming instructions configurable to cause a processorin a land vehicle to perform a method for using Synthetic Aperture Radar(SAR) to perform a maneuver with the land vehicle, the methodcomprising: accumulating a plurality of frames of the digitized radarreturn data; applying a RADON transform to the accumulated plurality offrames of the digitized radar return data and odometry data from theland vehicle to generate transformed frames of data for eachthree-dimensional point, wherein the RADON transform is configured toperform coherent integration for each three-dimensional point for whicha radar return exists from the pulsed radar transmission, project aradar trajectory onto each three-dimensional point, and project Dopplerinformation onto each three-dimensional point; generating atwo-dimensional X-Y map of an area covered by the pulsed radartransmission from the SAR based on the transformed frames of data foreach three-dimensional point; and performing an autonomous orsemiautonomous maneuver with the land vehicle by applying the generatedtwo-dimensional X-Y map.
 16. The non-transitory computer readable mediaof claim 15, wherein the RADON transform comprises a range dimension, aDoppler dimension, and a phase dimension.
 17. The non-transitorycomputer readable media of claim 16, wherein the RADON transform isrepresented by:${S\left( {x,y,z} \right)} = {\sum\limits_{f = 0}^{F - 1}{\sum\limits_{v = 0}^{V - 1}{\sum\limits_{h = 0}^{H - 1}{\sum\limits_{m = 0}^{M - 1}{\sum\limits_{n = 0}^{N - 1}{{s\left( {n,m,h,f} \right)}e^{{- 2}\pi j{R({m,f,x,y,z})}\frac{n}{N}}e^{{- 2}\pi j{D({m,f,x,y,z})}\frac{m}{M}}e^{{- 2}\pi j{P({m,h,v,f,x,y,z})}}}}}}}}$wherein: R(m, f, x, y, z) represents the range dimension, D(m, f, x, y,z) represents the Doppler dimension, P(m, h, f, x, y, z) represents thephase dimension, m=sample index, n=chirp index, h=horizontal antennaindex, v=vertical antenna index, f=frame index, x=x-axis location,y=y-axis location, z=z-axis location, s=sampled signal, N=number ofsamples, M=number of chirps, H=number of horizontal antennas, V=numberof vertical antennas, and F=number of frames.
 18. The non-transitorycomputer readable media of claim 17, wherein the range dimension of theRADON transform is represented by:${R\left( {m,f,x,y,z} \right)} = {\frac{2\alpha}{c}\sqrt{\left( {{O_{x}\left( {t\left( {m,f} \right)} \right)} - x} \right)^{2} + \left( {{O_{y}\left( {t\left( {m,f} \right)} \right)} - y} \right)^{2} + \left( {{O_{z}\left( {t\left( {m,f} \right)} \right)} - z} \right)^{2}}}$wherein: c=speed of light, α=chirp slope, t(m,f)=mT_(c)+fT_(f)T_(c)=Chirp repetition interval, T_(f)=Frame repetitioninterval, O_(x)=Odometry based vehicle position at the x-axis,O_(y)=Odometry based vehicle position at the y-axis, and O_(z)=Odometrybased vehicle position at the z-axis.
 19. The non-transitory computerreadable media of claim 17, wherein the Doppler dimension of the RADONtransform is represented by:${D\left( {m,f,x,y,z} \right)} = {\frac{2}{\lambda}\frac{\begin{matrix}{{\left. {{O_{x}\left( {t\left( {m,f} \right)} \right)} - x} \right)O_{Vx}} +} \\{{\left( {{O_{y}\left( {t\left( {m,f} \right)} \right)} - y} \right)O_{Vy}} + {\left( {{O_{z}\left( {t\left( {m,f} \right)} \right)} - z} \right)O_{Vz}}}\end{matrix}}{\sqrt{\left( {{O_{x}\left( {t\left( {m,f} \right)} \right)} - x} \right)^{2} + \left( {{O_{y}\left( {t\left( {m,f} \right)} \right)} - y} \right)^{2} + \left( {{O_{z}\left( {t\left( {m,f} \right)} \right)} - z} \right)^{2}}}}$wherein: t(m, f)=mT_(c)+fT_(f), λ=signal wavelength, T_(c)=Chirprepetition interval, T_(f)=Frame repetition interval, O_(x)=Odometrybased vehicle position at the x-axis, O_(y)=Odometry based vehicleposition at the y-axis, O_(z)=Odometry based vehicle position at thez-axis, O_(Vx)=Odometry based vehicle velocity at the x-axis,O_(Vy)=Odometry based vehicle velocity at the y-axis, andO_(Vz)=Odometry based vehicle velocity at the z-axis.
 20. Thenon-transitory computer readable media of claim 17, wherein the phasedimension of the RADON transform is represented by:${P\left( {m,h,f,x,y,z} \right)} = {{\frac{\frac{\left. {{O_{y}\left( {t\left( {m,f} \right)} \right)} - y} \right)}{\left. {{O_{x}\left( {t\left( {m,f} \right)} \right)} - x} \right)}}{\begin{matrix}\sqrt{1 + \left( \frac{\left. {{O_{y}\left( {t\left( {m,f} \right)} \right)} - y} \right)}{\left. {{O_{x}\left( {t\left( {m,f} \right)} \right)} - x} \right)} \right)^{2}} \\\sqrt{1 + \frac{\left( {{O_{z}\left( {t\left( {m,f} \right)} \right)} - z} \right)^{2}}{\left( {{O_{x}\left( {t\left( {m,f} \right)} \right)} - x} \right)^{2} + \left( {{O_{y}\left( {t\left( {m,f} \right)} \right)} - y} \right)^{2}}}\end{matrix}}h\frac{d_{h}}{\lambda}} + {\frac{\frac{{O_{z}\left( {t\left( {m,f} \right)} \right)} - z}{\sqrt{\left. {\left. \left( {{O_{x}\left( {t\left( {m,f} \right)} \right)} - x} \right) \right)^{2} + \left( {{O_{y}\left( {t\left( {m,f} \right)} \right)} - y} \right)} \right)^{2}}}}{\sqrt{1 + \frac{\left( {{O_{z}\left( {t\left( {m,f} \right)} \right)} - z} \right)^{2}}{\left. {\left. \left( {{O_{x}\left( {t\left( {m,f} \right)} \right)} - x} \right) \right)^{2} + \left( {{O_{y}\left( {t\left( {m,f} \right)} \right)} - y} \right)} \right)^{2}}}}v\frac{d_{v}}{\lambda}}}$wherein: t(m, f)=mT_(c)+fT_(f), λ=signal wavelength, d_(h)=antennahorizontal spacing, d_(v)=antenna vertical spacing, T_(c)=Chirprepetition interval, T_(f)=Frame repetition interval, O_(x)=Odometrybased vehicle position at the x-axis, O_(y)=Odometry based vehicleposition at the y-axis, O_(z)=Odometry based vehicle position at thez-axis, O_(Vx)=Odometry based vehicle velocity at the x-axis,O_(Vy)=Odometry based vehicle velocity at the y-axis, andO_(Vz)=Odometry based vehicle velocity at the z-axis.